论文标题
在两个laplacian矩阵上用于偏斜的增益图
On Two Laplacian Matrices for Skew Gain Graphs
论文作者
论文摘要
令$ g =（v，\ oferrightArrow {e}）$为一个图形，边缘有一些规定的方向，而$γ$是任意组。如果$ f \ in \ mathrm {inv}（γ）$是反侵入的，那么偏差增益图$φ_f=（g，γ，φ，f）$是这样的偏差增益函数$φ：\ overrightArrow {e} \rightarrowγ$满足$φ（\ oferrightArrow {vu}）= f（φ（\ oftrightArrow {uv}））$。在本文中，我们研究了两种不同类型的类型：偏斜增益图的laplacian和$ g $ -laplacian矩阵，其中从特征性零的field $ f $ f $ f $ f $ f $ f $ f $ f。定义入射率矩阵，我们还证明了在$ g $ -laplacian矩阵的情况下，矩阵定理用于偏斜增益图。
Let $G=(V,\overrightarrow{E})$ be a graph with some prescribed orientation for the edges and $Γ$ be an arbitrary group. If $f\in \mathrm{Inv}(Γ)$ be an anti-involution then the skew gain graph $Φ_f=(G,Γ,φ,f)$ is such that the skew gain function $φ:\overrightarrow{E}\rightarrow Γ$ satisfies $φ(\overrightarrow{vu})=f(φ(\overrightarrow{uv}))$. In this paper, we study two different types, Laplacian and $g$-Laplacian matrices for a skew gain graph where the skew gains are taken from the multiplicative group $F^\times$ of a field $F$ of characteristic zero. Defining incidence matrix, we also prove the matrix tree theorem for skew gain graphs in the case of the $g$-Laplacian matrix.
